The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
1answer
222 views

Concept of synchronizability

This thread is about the concept of synchronizability. It's a concept I tried to formalize in its most general sense but without success. The goal of this thread is therefore to try to formalize it in ...
-1
votes
1answer
54 views

Idempotent solutions to the implict function theorem other than the identity?

I am interested in the following problem. Assume that an (anti)symmetric function $g:\mathbb{R}^2 \to \mathbb{R}$ satisfies the implicit function theorem. That is, $g(x,y) = \pm g(y,x)$ and $g(x,y)=0$ ...
12
votes
0answers
359 views

Which limit to take as a key applied math decision

The Borel-Kolmogorov paradox refers to situations where non-uniqueness in the notion of conditioning on a set of measure zero leads to apparent contradictions. As a formal matter, one requires ...
4
votes
0answers
245 views

Seminar Notes Repository

On Seminars, people actually talk a lot more about motivations than when they write in paper. It would be a good idea if there is an online repository where people can upload notes (handwritten, ...
3
votes
0answers
119 views

Reference request: name of a transform

Define a transform on polynomials which is linear and acts on each monomial as $$\widehat{z^k} = \frac{(1+z)(2+z)\ldots(k+z)}{k!}.$$ Does anyone know whether this has a name (and therefore has been ...
2
votes
0answers
47 views

Find Moment condition for generalized method of moments

Consider a scalar system with 2K outputs and K+2 unknowns $y_{k,1}=x_ka_1+n_{k,1} \quad y_{k,2}=x_ka_2+n_{k,1}$. The variables $n_{k,\ell}$ are zero mean noise variables. To estimate $a_1$ and $a_2$, ...
2
votes
0answers
97 views

Jacobi triple product for multidimensional lattices

The Jacobi triple product identity gives as a special case a product formula for the theta function of a 1-dimensional lattice. Is there a more general product formula for the theta function of an ...
2
votes
0answers
175 views

Finite topological dimension x local compactness

Of course, the two notions are independent one from the other, but often one of them implies the other under some additional hypotheses. For instance: A topological vector space is finite dimensional ...
1
vote
0answers
121 views

General procedure to find the determinant of an operator?

I want to learn to find the determinant of an operator. I am given an operator like $\Sigma _{\alpha\beta}=-k^2g_{\alpha\beta}+i\theta\epsilon_{\alpha\beta\gamma} k^\gamma$ $k^2=k^μk_μ$, $g^{αβ}$ ...
1
vote
0answers
338 views

Conjectures on fractions where each digit appears once in numerator and denominator

This is a highly redacted version of a question that was asked before. Please see Criteria of considering relevance of the question to the domain of research topics for details. Some numerical ...
1
vote
0answers
114 views

Reference needed for: Automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning

I am doing research on automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning. I have found several research papers on ...
1
vote
0answers
306 views

Allocation game optimal strategy

There are two players, Alice and Bob. There is an initial pool of 100 dollars. Alice proposes an allocation of the dollars (real numbers, not necessarily integers), and Bob can either accept or ...
1
vote
0answers
166 views

Regarding a Feature of Multivariate Real Function

Any real function can be expressed as a function of the sum of two monotonic real functions? More precisely, for real function p(x, y), there exist continuous real functions P(x), h(x,y), g(x) such ...
0
votes
0answers
85 views

Asymptotic inverses of asymptotic functions

The prime number theorem states that two functions are asymptotic. Their inverses (as functions of an integral variable) are also asymptotic. In general, under what conditions are the inverses of ...
0
votes
0answers
95 views

Repeated function resulting in quadratic time.

Let $$r(f, x) = k$$ such that $$f^k (x) < 2 \hbox{ and } f^{k-1} (x) \geq 2$$ For example $$r(n \rightarrow n-1, 2^n) = 2^n-1; r(n \rightarrow n/2, 2^n) = n.$$ For an arbitrary $c$, we have $$r( ...